We have performed AIMD simulations by using the Car-Parrinello molecular dynamics method [1]}
implemented in the Quantum ESPRESSO package. [2]}
We used 63 water molecules and a hydroxide or hydronium ion
in a periodic cubic cell with a length of 12.4447 Å.
A kinetic energy cutoff of 85 Ry was adopted.
We used the meta-GGA exchange-correlation functional in the form of SCAN [3]}
and the Hamann-Schl\(\ddot{u}\) ter-Chiang-Vanderbilt pseudopotentials
generated with the PBE functional. [4]}
For the AIMD simulations, we adopted the Nosé-Hoover chain thermostats with a chain length
of 4 for each ion to control the temperature of 330 K in the NVT ensemble. [5]}, [6]}, [7]}
The mass of hydrogen atom was set to 2.0141 (mass of deuterium).
A fictitious electron mass of 100 a.u. was used along with a mass cut-off of 25 a.u.
The AIMD trajectory lengths were 124.4 and 176.9 ps for the hydroxide and hydronium simulations, respectively. A time step of 2.0 a.u was adopted.
AIMD results utilizing the PBE0-TS XC functional referenced
from literature [8]}
were also shown, which serve as a baseline to
elucidate the effects of the SCAN functional in predicting properties of
hydronium and hydroxide in an aqueous environment.
A standard hydrogen bond criterion was adopted[9]}.
Specifically, two neighboring water molecules are defined to be H-bonded when
the O-O distance is less than 3.5 \(\rm Å\) ,
the inter-water O-H distance is less than 1.24 \(\rm Å\) ,
and the O-O-H angle is less than \(30^{\circ }\) .
<FIGURE><FIGURE>